Systems are known for determining the general direction and trajectory of projectiles, such as bullets emanating from unfriendly small arms fire. One such system, described in U.S. Pat. No. 5,241,518 ("the '518 patent"), is comprised of at least three spaced-apart sensors, which are positioned to encounter the shock wave generated by a supersonic projectile. The sensors generate signals in response to the shock wave which are related to the azimuth and elevation angle of a unit sighting vector from each sensor to the origin of the shock wave. A unit vector, while having direction, has no magnitude (representative of distance in this case). Thus, the distance from each sensor to the origin of the shock wave and, hence, the trajectory remains unknown. The unit sighting vectors could point to a large number of possible actual trajectories.
It is disclosed in the '518 patent that each unit sighting vector makes the same angle with the trajectory no matter what the azimuth or elevation angle of the trajectory is, so that instead of a number of possible trajectory solutions, only one actual trajectory solution may be calculated.
The three sensors in the '518 patent implementation are capable of sequentially generating a signal in response to sequential pressure on each transducer, created by the shock wave as it encounters each transducer. The three transducers in each sensor, therefore, produce a signal which is related to the azimuth and elevation angle of a unit sighting vector for each sensor. With a combination of three such sensors, three reasonably accurate unit sighting vectors to the origin of the shock wave and hence the trajectory of the projectile can be determined.
In the embodiment, disclosed in the '518 patent, the unit sighting vectors of each sensor are determined by measuring the time when the shock wave encounters each of the transducers in a sensor. This time relationship of the three transducers provides a unit sighting vector from the sensor to the trajectory of the projectile. Based on the assumption that these unit sighting vectors form the same angle with the trajectory, the magnitude (distance in this case) of the unit sighting vectors is calculated. With the magnitude being calculated for each sensor, three points in space are defined. These three points in space will define the azimuth and elevation angle of the local trajectory of the projectile, and also an intercept with an arbitrary plane in a coordinate system. Further, with the sensors arranged as described in the '518 patent, the velocity of the projectile may be determined, and by determining the time lapse of the passing of the main shock front and an ambient density line of the projectile over the sensors, the length of the projectile can also be calculated. It is disclosed in the '518 patent, that the intensity of the main shock front, normalized to the miss-distance (i.e., the length or magnitude of the unit sighting vector), the projectile velocity, and the length of the projectile provide sufficient information so that, from known projectile characteristics (i.e. known ballistic profiles), the likely projectile itself can be determined. By knowing the projectile and its specific characteristics, and having determined its local velocity and the local trajectory, the entire trajectory can be calculated. This provides a close approximation of the position of the origin of that projectile.
Disadvantageously, the methodology described in the '518 patent requires that the sensors be relatively closely spaced in order to accommodate the known ballistic model used, which assumes that the projectile passes each sensor element at the same speed. Thus, wide spacing of the sensors using the methodology according to the '518 patent can lead to erroneous readings and false indications as to the origin of the projectile. Further, the approach described in the '518 patent uses only the shock wave produced by the projectile as it travels. The shock wave is used to extrapolate the trajectory of the projectile based on a few points in space and the time it takes the shock wave to reach those points. No use is made of information pertaining to the muzzle blast, i.e. the initial blast wave generated as the projectile is fired. Rather, the origin of the blast wave is determined based on the extrapolation of the projectile trajectory and the estimated characteristics of the projectile, which are subject to errors.
Another known system utilizes a blast wave from a fired projectile to determine the origin of the projectile, as described in U.S. Pat. No. 5,544,129 ("the '129 patent"). The system in the '129 patent is based on detection of the blast wave generated, for example, by the muzzle blast from the gun firing the projectile. The system in the '129 patent is not based on data from the projectile itself, as is the aforementioned U.S. patent, but it is based only on the data collected from the blast wave of, for example, the muzzle blast of a gun firing a bullet.
The '129 patent depends on the signals generated by the transducers forming time relationships between the transducers when the blast wave serially encounters each of three required transducers. From these time relationships, at least one unit sighting vector is determined from at least one sensor to the origin of the blast wave and that unit sighting vector is considered to point in the general direction of the origin of the projectile.
When at least two spaced-apart sensors each generates a unit sighting vector, then those two unit sighting vectors are used to determine, via a triangulation calculation, the general distance from the sensors to the origin of the projectile. Thus, by having not only the general direction of the origin of the blast wave from the sensors, but also having the general distance of the origin of the blast wave from the sensors, the location of the sniper, assassin, criminal, etc., is determined.
The '129 patent methodology uses only the muzzle blast to determine the general origin of the projectile, it does not use the shock wave at all. Disadvantageously, the acoustic signal representative of muzzle blast can easily be corrupted after it is generated, such as by attenuation or distortion introduced by structures, e.g. buildings, topology etc, in the path of the blast as it travels toward the sensors. Similarly, in a reverberant environment, multipath arrivals of the shock wave can obscure the blast wave, which always arrives later than the shock wave. A muzzle blast waveform tends to have a lower signal to noise ratio making it difficult to precisely measure its time of arrival. Moreover, silenced weapons fire will go undetected by a system such as in the '129 patent where only muzzle blast is used to determine the general origin of a supersonic projectile.
Another counter-sniper system, implemented by Science Applications International Corporation, is described in a publication entitled SAIC SENTINEL ACOUSTIC COUNTER-SNIPER SYSTEM, published in SPIE International Symposium Proceedings Vol. 2938, 1996 ("the Sentinel system"). The Sentinel system is comprised of two arrays of microphones separated by a selected distance, which provide muzzle blast and shock wave information to signal processing circuitry. Although the Sentinel system is operable with only a single array of microphones, the two array configuration is implemented to provide validity checking, redundancy and qualification. The two separate volumetric arrays each observe shock direction of arrival; shock arrival time; blast direction of arrival; blast arrival time; shock waveform period; and shock waveform amplitude. Based on these observed phenomena, signal processing circuitry is configured to derive azimuth and elevation to the shooter; range to the shooter; trajectory of the projectile; caliber of the projectile; and muzzle velocity. High algorithmic complexity and sophistication is implemented to effect these derivations.
Generally, in the Sentinel system each detected event is classified as shock, blast, or false alarm based on its waveform amplitude, period, and bandwidth. Then, shock events at each array are grouped by temporal proximity into wavefront arrivals, and similarly for blast events. These groups are then fit to plane waves, iteratively rejecting outliers and saving residuals for later confidence assessment. Median shock waveform amplitude and period for each shock wavefront are used to determine caliber and miss distance, which are then iteratively refined to solve for range and muzzle velocity. Range is determined by iterative solution of the equations relating shock and blast arrival directions and arrival time difference, muzzle velocity, projectile caliber, which in turn gives drag coefficient, and trajectory. Bearing is determined either from blast wave direction of arrival, or inferred from the trajectory and range.
Disadvantageously, the Sentinel system requires direct acoustic path measurements from both the shock wave and the muzzle blast to obtain the trajectory or the projectile origin estimate. Additionally, corruption of the muzzle data direction of arrival by shock wave multipath degrades the estimates greatly. The SAIC Sentinel System also requires a very high sample rate, high precision electronics and high quality microphones, and relatively high amounts of computational power. The need for such sophisticated components adds significant cost to the Sentinel system, and raises issues as to applications in harsh environments. It also does not use robust solution algorithms which automatically edit out bad or missing data without computation intensive conditional branching to special cases.